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Answer :
To solve the problem of writing [tex]\(740\%\)[/tex] as both a decimal and a mixed number, we need to follow these steps:
### 1. Writing [tex]\(740\%\)[/tex] as a Decimal:
To convert a percentage to a decimal, divide the percentage by 100.
[tex]\[
740\% = \frac{740}{100} = 7.4
\][/tex]
So, [tex]\(740\%\)[/tex] as a decimal is [tex]\(7.4\)[/tex].
### 2. Writing [tex]\(740\%\)[/tex] as a Mixed Number:
A percentage can also be expressed as a fraction, which can then be simplified or converted to a mixed number.
First, we note:
[tex]\[
740\% = \frac{740}{100}
\][/tex]
We can divide the numerator by the denominator:
- The whole number part is obtained by performing integer division of the numerator by the denominator:
[tex]\[
\text{Whole number part} = \left\lfloor \frac{740}{100} \right\rfloor = 7
\][/tex]
- The fractional part is obtained by taking the remainder of the division:
[tex]\[
\text{Remainder} = 740 \mod 100 = 40
\][/tex]
This means we have:
[tex]\[
740\% = 7 \frac{40}{100}
\][/tex]
Next, we simplify the fraction [tex]\(\frac{40}{100}\)[/tex]. To do this, we divide the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 40 and 100 is 20.
So, we simplify [tex]\(\frac{40}{100}\)[/tex] as follows:
[tex]\[
\frac{40 \div 20}{100 \div 20} = \frac{2}{5}
\][/tex]
Therefore, the mixed number representation of [tex]\(740\%\)[/tex] is:
[tex]\[
7 \frac{2}{5}
\][/tex]
### Final Answer:
- The decimal representation of [tex]\(740\%\)[/tex] is [tex]\(7.4\)[/tex].
- The mixed number representation of [tex]\(740\%\)[/tex] is [tex]\(7 \frac{2}{5}\)[/tex].
So, the correct answer from the given options is:
[tex]\[
7.4 \text{ and } 7 \frac{2}{5}
\][/tex]
### 1. Writing [tex]\(740\%\)[/tex] as a Decimal:
To convert a percentage to a decimal, divide the percentage by 100.
[tex]\[
740\% = \frac{740}{100} = 7.4
\][/tex]
So, [tex]\(740\%\)[/tex] as a decimal is [tex]\(7.4\)[/tex].
### 2. Writing [tex]\(740\%\)[/tex] as a Mixed Number:
A percentage can also be expressed as a fraction, which can then be simplified or converted to a mixed number.
First, we note:
[tex]\[
740\% = \frac{740}{100}
\][/tex]
We can divide the numerator by the denominator:
- The whole number part is obtained by performing integer division of the numerator by the denominator:
[tex]\[
\text{Whole number part} = \left\lfloor \frac{740}{100} \right\rfloor = 7
\][/tex]
- The fractional part is obtained by taking the remainder of the division:
[tex]\[
\text{Remainder} = 740 \mod 100 = 40
\][/tex]
This means we have:
[tex]\[
740\% = 7 \frac{40}{100}
\][/tex]
Next, we simplify the fraction [tex]\(\frac{40}{100}\)[/tex]. To do this, we divide the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 40 and 100 is 20.
So, we simplify [tex]\(\frac{40}{100}\)[/tex] as follows:
[tex]\[
\frac{40 \div 20}{100 \div 20} = \frac{2}{5}
\][/tex]
Therefore, the mixed number representation of [tex]\(740\%\)[/tex] is:
[tex]\[
7 \frac{2}{5}
\][/tex]
### Final Answer:
- The decimal representation of [tex]\(740\%\)[/tex] is [tex]\(7.4\)[/tex].
- The mixed number representation of [tex]\(740\%\)[/tex] is [tex]\(7 \frac{2}{5}\)[/tex].
So, the correct answer from the given options is:
[tex]\[
7.4 \text{ and } 7 \frac{2}{5}
\][/tex]
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